Finding W and Theta in Simultaneous Equations

In summary, the student is trying to solve for W using cos(θ), however they are having trouble simplifying the theta with the sin and cos attached.
  • #1
camino
42
0

Homework Statement



160 cos(theta) - W cos(69) = 0

160 sin(theta) - W cos(21) - W = 0

Can someone solve these equations for me to find W and theta?
 
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  • #2
camino said:

Homework Statement



160 cos(theta) - W cos(69) = 0

160cosθ=Wcos(69)

W=160cosθ/cos(69)


continue now
 
  • #3
W = W cos(69) / cos(69)?
 
  • #4
camino said:
W = W cos(69) / cos(69)


?

no, put W=160cosθ/cos(69) into the second equation
 
  • #5
Sorry I am still not seeing it. Could you give me one more step?
 
  • #6
camino said:
Sorry I am still not seeing it. Could you give me one more step?

In this equation

160 sinθ - W cos(21) - W = 0


everywhere you see 'W' put 160cosθ/cos(69) and try to simplify it.
 
  • #7
I do understand how to simplify one equation and substitute into the other, however I just can't seem to simplify these down. The theta with the sin and cos attached is what is really confusing me when trying to simplify. This is just a mess and I'm very confused.
 
  • #8
camino said:
I do understand how to simplify one equation and substitute into the other, however I just can't seem to simplify these down. The theta with the sin and cos attached is what is really confusing me when trying to simplify. This is just a mess and I'm very confused.

just show where you've reached and we'll see if we can simplify it further
 
  • #9
160 sinθ - (160cosθ/cos69) cos(21) - (160cosθ/cos69) = 0
 
  • #10
camino said:
160 sinθ - (160cosθ/cos69) cos(21) - (160cosθ/cos69) = 0

so you get


[tex]160 sin \theta - (\frac{160cos21}{cos69} - \frac{160}{cos69})cos \theta = 0[/tex]


this is like Asinθ-Bcosθ=0, how do you solve this equation?
 
  • #11
Is there a trig identity that replaces either sin or cos? I'm thinking we want to narrow this down to only having either sin or cos in the equation.
 
  • #12
camino said:
Is there a trig identity that replaces either sin or cos? I'm thinking we want to narrow this down to only having either sin or cos in the equation.

well yes but we can put it like this


Asinθ=Bcosθ

or sinθ/cosθ=B/A

do we know another way to express sinθ/cosθ ?
 
  • #13
I am really not sure.
 
  • #14
camino said:
I am really not sure.

do you not know that tanθ=sinθ/cosθ ?
 
  • #15
Oh my it has been a long day.. Yes i see that now. So simplifying I would then do:

160 sinθ - (-29.6542) cosθ = 0

160 sinθ = 29.6542 cosθ

θ = tan^-1(160/29.6542)

θ = 79.5° ?
 
  • #16
camino said:
Oh my it has been a long day.. Yes i see that now. So simplifying I would then do:

160 sinθ - (-29.6542) cosθ = 0

160 sinθ = 29.6542 cosθ

θ = tan^-1(160/29.6542)

θ = 79.5° ?

yes that should be correct. You are able to find W knowing θ=79.5° right?
 
  • #17
Yes:

160cos(79.5) - W cos(69) = 0

29.1577 = W cos(69)

W = 81.36
 
  • #18
Thank you so much for all your help!
 

What are simultaneous equations?

Simultaneous equations are a set of two or more equations that are solved at the same time in order to find the values of the unknown variables that satisfy all of the equations.

How are simultaneous equations solved?

Simultaneous equations can be solved using several methods such as substitution, elimination, or graphing. These methods involve manipulating the equations to eliminate one of the variables and then solving for the remaining variable.

What is the importance of simultaneous equations in science?

Simultaneous equations are used in various scientific fields, such as physics, chemistry, and engineering, to model and solve real-world problems. They allow us to find the relationships between different variables and make predictions based on those relationships.

What are some common applications of simultaneous equations?

Simultaneous equations are commonly used to solve problems involving speed, distance, and time; chemical reactions; and electrical circuits. They can also be used to analyze data and make predictions in various scientific experiments and studies.

What are some tips for solving simultaneous equations?

Some tips for solving simultaneous equations include choosing a method that best suits the given equations, carefully manipulating the equations to eliminate a variable, and checking the solutions by substituting them back into the original equations. It is also helpful to clearly label and organize the equations and steps of the solution.

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